power-spectral-density

DERIVED_FROM is not applicable here — this is INSTANCE_OF. power-spectral-density IS a specific kind of spectral representation: it presents signal power as a function of frequency. A competent speaker would call PSD 'a spectral representation'. Files against the nearest kind.

power-spectral-density IS a specific kind of spectral-density: it measures power distribution across frequency for stationary signals. PSD is a specific instance of the broader spectral-density concept. Specific→general per Law 9.

PSD is computed as the squared magnitude |X(f)|² of spectral coefficients. Spectral magnitude came first: PSD is derived from it by squaring. Without spectral magnitude, PSD has no foundation.

MFCC computation operates on the power spectral density as its primary input: the pipeline extracts the PSD (or power spectrum), applies mel-scale filterbank, takes log, then DCT. Remove power-spectral-density as a concept and MFCC has nothing to operate on — it cannot function. DEPENDS_ON (Law 8 removal test).

The cepstrum is computed by taking the FFT of the log power spectrum: cepstrum = IDFT(log(PSD)). Remove power-spectral-density and the cepstrum has no input — it stops operating. DEPENDS_ON (Law 8 removal test).

Spectral energy (the integral or sum of spectral power across all frequencies) is derived from the power spectral density. The PSD concept existed first and provided the mathematical basis: spectral energy = integral of PSD over frequency. DERIVED_FROM historical test passes — the general concept of PSD predates the specific metric of total spectral energy.

The periodogram is a spectral estimation technique whose sole purpose is to produce an estimate of the power spectral density. Periodogram did not exist before PSD — it is defined as a method to estimate PSD. Which came first? The concept of spectral power density came first; the periodogram was invented to derive it.

White noise is defined by its power spectral density (flat PSD). The concept of PSD existed first and provided the framework for defining white noise as a signal with constant PSD. Per Law 7: which existed first?

Pink noise is defined by its 1/f power spectral density. The PSD concept predates and enables the definition of pink noise. Per Law 7: PSD existed first and fed into noise classification.

Spectral whitening operates directly on the power spectral density — it reshapes the PSD to achieve flatness. Remove the concept of PSD and spectral whitening has no object to operate on, no measurable quantity to target. The removal test passes.